%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO220+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:14:49 AM UTC 2026
% Result : Theorem 10.40s 3.41s
% Output : CNFRefutation 10.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 5 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(couo1,axiom,
! [X0,X1,X2] :
( ( ~ 'unorthogonal$ulines'(X0,X2)
& ~ 'unorthogonal$ulines'(X0,X1) )
=> ~ 'convergent$ulines'(X1,X2) ) ).
fof(a3,axiom,
! [X0,X1] :
( 'parallel$ulines'(X0,X1)
<=> ~ 'convergent$ulines'(X0,X1) ) ).
fof(a5,axiom,
! [X0,X1] :
( 'orthogonal$ulines'(X0,X1)
<=> ~ 'unorthogonal$ulines'(X0,X1) ) ).
fof(con,conjecture,
! [X0,X1,X2] :
( ( 'orthogonal$ulines'(X0,X2)
& 'orthogonal$ulines'(X0,X1) )
=> 'parallel$ulines'(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'orthogonal$ulines'(X0,X2)
& 'orthogonal$ulines'(X0,X1) )
=> 'parallel$ulines'(X1,X2) ),
inference(negate_conjecture,[status(cth)],[con]) ).
cnf(c31,plain,
( ~ 'convergent$ulines'(X1,X2)
| 'unorthogonal$ulines'(X0,X2)
| 'unorthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[couo1]) ).
cnf(c41,plain,
( 'convergent$ulines'(X0,X1)
| 'parallel$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a3]) ).
cnf(c44,plain,
( ~ 'unorthogonal$ulines'(X0,X1)
| ~ 'orthogonal$ulines'(X0,X1) ),
inference(clausification,[status(esa)],[a5]) ).
cnf(c46,plain,
'orthogonal$ulines'(sK81,sK82),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
'orthogonal$ulines'(sK81,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c48,plain,
~ 'parallel$ulines'(sK82,sK83),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'convergent$ulines'(sK82,sK83),
inference(resolution,[status(thm)],[c41,c48]) ).
cnf(d1,plain,
( 'unorthogonal$ulines'(X0,sK82)
| 'unorthogonal$ulines'(X0,sK83) ),
inference(resolution,[status(thm)],[c31,d0]) ).
cnf(d2,plain,
~ 'unorthogonal$ulines'(sK81,sK83),
inference(resolution,[status(thm)],[c44,c47]) ).
cnf(d3,plain,
'unorthogonal$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
~ 'unorthogonal$ulines'(sK81,sK82),
inference(resolution,[status(thm)],[c44,c46]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO220+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:07:44 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.40/3.41 % SZS status Theorem for theBenchmark.p
% 10.40/3.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------